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The convex function determined by a multifunction

Published online by Cambridge University Press:  17 April 2009

M. Coodey  and
S. Simons
M. Coodey
Affiliation:
Department of Mathematics, University of California, Santa Barbara CA 93106-3080, United States of America
S. Simons
Affiliation:
Department of Mathematics, University of California, Santa Barbara CA 93106-3080, United States of America
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Abstract

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We shall show how each multifunction on a Banach space determines a convex function that gives a considerable amount of information about the structure of the multifunction. Using standard results on convex functions and a standard minimax theorem, we strengthen known results on the local boundedness of a monotone operator, and the convexity of the interior and closure of the domain of a maximal monotone operator. In addition, we prove that any point surrounded by (in a sense made precise) the convex hull of the domain of a maximal monotone operator is automatically in the interior of the domain, thus settling an open problem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 1 , August 1996 , pp. 87 - 97
Copyright
Copyright © Australian Mathematical Society 1996

References

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